Optimization of turbine design in wind farms with multiple hub heights,using exact analytic gradients and structural constraints

Wind farms are generally designed with turbines of all the same hub height. If wind farms were designed with turbines of different hub heights, wake interference between turbines could be reduced, lowering the cost of energy (COE). This paper demonstrates a method to optimize onshore wind farms with two different hub heights using exact, analytic gradients. Gradient‐based optimization with exact gradients scales well with large problems and is preferable in this application over gradient‐free methods. Our model consisted of the following: a version of the FLOw Redirection and Induction in Steady‐State wake model that accommodated three‐dimensional wakes and calculated annual energy production, a wind farm cost model, and a tower structural model, which provided constraints during optimization. Structural constraints were important to keep tower heights realistic and account for additional mass required from taller towers and higher wind speeds. We optimized several wind farms with tower height, diameter, and shell thickness as coupled design variables. Our results indicate that wind farms with small rotors, low wind shear, and closely spaced turbines can benefit from having two different hub heights. A nine‐by‐nine grid wind farm with 70‐meter rotor diameters and a wind shear exponent of 0.08 realized a 4.9% reduction in COE by using two different tower sizes. If the turbine spacing was reduced to 3 diameters, the reduction in COE decreased further to 11.2%. Allowing for more than two different turbine heights is only slightly more beneficial than two heights and is likely not worth the added complexity.     

Large eddy simulations of the effect of vertical staggering in large wind farms

In order to study the effect of vertical staggering in large wind farms, large eddy simulations (LES) of large wind farms with a regular turbine layout aligned with the given wind direction were conducted. In the simulations, we varied the hub heights of consecutive downstream rows to create vertically staggered wind farms. We analysed the effect of streamwise and spanwise turbine spacing, the wind farm layout, the turbine rotor diameter, and hub height difference between consecutive downstream turbine rows on the average power output. We find that vertical staggering significantly increases the power production in the entrance region of large wind farms and is more effective when the streamwise turbine spacing and turbine diameter are smaller. Surprisingly, vertical staggering does not significantly improve the power production in the fully developed regime of the wind farm. The reason is that the downward vertical kinetic energy flux, which brings high velocity fluid from above the wind farm towards the hub height plane, does not increase due to vertical staggering. Thus, the shorter wind turbines are effectively sheltered from the atmospheric flow above the wind farm that supplies the energy, which limits the benefit of vertical staggering. In some cases, a vertically staggered wind farm even produced less power than the corresponding non vertically staggered reference wind farm. In such cases, the production of shorter turbines is significantly negatively impacted while the production of the taller turbine is only increased marginally.     

Self‐similarity and turbulence characteristics of wind turbine wakes via large‐eddy simulation

Mean and turbulent properties of the wake generated by a single wind turbine are studied in this paper with a new large eddy simulation (LES) code, the wind turbine and turbulence simulator (WiTTS hereafter). WiTTS uses a scale‐dependent Lagrangian dynamical model of the sub‐grid shear stress and actuator lines to simulate the effects of the rotating blades. WiTTS is first tested by simulating neutral boundary layers without and with a wind turbine and then used to study the common assumptions of self‐similarity and axisymmetry of the wake under neutral conditions for a variety of wind speeds and turbine properties. We find that the wind velocity deficit generally remains self similarity to a Gaussian distribution in the horizontal. In the vertical, the Gaussian self‐similarity is still valid in the upper part of the wake, but it breaks down in the region of the wake close to the ground. The horizontal expansion of the wake is always faster and greater than the vertical expansion under neutral stability due to wind shear and impact with the ground. Two modifications to existing equations for the mean velocity deficit and the maximum added turbulence intensity are proposed and successfully tested. The anisotropic wake expansion is taken into account in the modified model of the mean velocity deficit. Turbulent kinetic energy (TKE) budgets show that production and advection exceed dissipation and turbulent transport. The nacelle causes significant increase of every term in the TKE budget in the near wake. In conclusion, WiTTS performs satisfactorily in the rotor region of wind turbine wakes under neutral stability. Copyright © 2014 John Wiley & Sons, Ltd.     

Effects of turbine spacing on the power output of extended wind‐farms

We present results from large eddy simulations of extended wind‐farms for several turbine configurations with a range of different spanwise and streamwise spacing combinations. The results show that for wind‐farms arranged in a staggered configuration with spanwise spacings in the range ≈[3.5,8]D, where D is the turbine diameter, the power output in the fully developed regime depends primarily on the geometric mean of the spanwise and streamwise turbine spacings. In contrast, for the aligned configuration the power output in the fully developed regime strongly depends on the streamwise turbine spacing and shows weak dependence on the spanwise spacing. Of interest to the rate of wake recovery, we find that the power output is well correlated with the vertical kinetic energy flux, which is a measure of how much kinetic energy is transferred into the wind‐turbine region by the mean flow. A comparison between the aligned and staggered configurations reveals that the vertical kinetic energy flux is more localized along turbine columns for aligned wind‐farms than for staggered ones. This additional mixing leads to a relatively fast wake recovery for aligned wind‐farms. Copyright © 2015 John Wiley & Sons, Ltd.     

Wind turbine boundary layer arrays for Cartesian and staggered configurations‐Part I,flow field and power measurements

Model wind turbine arrays were developed for the purpose of investigating the wake interaction and turbine canopy layer in a standard cartesian and row‐offset turbine array configurations. Stereographic particle image velocimetry was used to collect flow data upstream and downstream of entrance and exit row turbines in each configuration. Wakes for all cases were analyzed for energy content and recovery behavior including entrainment of high‐momentum flow from above the turbine canopy layer. The row‐offset arrangement of turbines within an array grants an increase in streamwise spacing of devices and allows for greater wake remediation between successive rows. These effects are seen in exit row turbine wakes as changes to statistical quantities including the in‐plane Reynolds stress, , and the production of turbulence. The recovery of wakes also strongly mitigates the perceived underperformance of wind turbines within an array. The flux of kinetic energy is demonstrated to be more localized in the entrance rows and in the offset arrangement. Extreme values for the flux of kinetic energy are about 7.5% less in the exit row of the cartesian arrangement than in the offset arrangement. Measurements of mechanical torque at entrance and exit row turbines lead to curves of power coefficient and demonstrate an increase in efficiency in row‐offset configurations. Copyright © 2014 John Wiley & Sons, Ltd.     

Dependence of optimal wind turbine spacing on wind farm length

Recent large eddy simulations have led to improved parameterizations of the effective roughness height of wind farms. This effective roughness height can be used to predict the wind velocity at hub‐height as function of the geometric mean of the spanwise and streamwise turbine spacings and the turbine loading factors. Recently, Meyers and Meneveau used these parameterizations to make predictions for the optimal wind turbine spacing in infinitely large wind farms. They found that for a realistic cost ratio between the turbines and the used land surface, the optimal turbine spacing may be considerably larger than that used in conventional wind farms. Here, we extend this analysis by taking the length of the wind farm, i.e. the number of rows in the downstream direction into account and show that the optimal turbine spacing strongly depends on the wind farm length. For small to moderately sized wind farms, the model predictions are consistent with spacings found in operational wind farms. For much larger wind farms, the extended optimal spacing found for infinite wind farms is confirmed. Copyright © 2015 John Wiley & Sons, Ltd.     

Turbulent kinetic energy estimates from profiling wind LiDAR measurements and their potential for wind energy applications

This study shows that turbulent kinetic energy (TKE) estimates, derived from static LiDARs in Doppler Beam Swing (DBS) mode, permit a qualitative and quantitative characterization and analysis of turbulent structures as wind turbine wakes, and convective or shear generated eddies in the lower atmospheric boundary layer. The analysed data, collected by a WINDCUBE™ v1 in a wind park in Austria, is compared to WINDCUBE™ v1 and sonic data from the WINd Turbine Wake EXperiment Wieringermeer (WINTWEX-W). Although turbulence measurements with a WINDCUBE™ v1 are limited to a specific length scale, processed measurements above this threshold are in a good agreement with sonic anemometer data. In contrast to the commonly used turbulence intensity, the calculation of TKE not only provides an appropriate measure of turbulence intensities but also gives an insight into its origin. The processed data show typical wake characteristics, as flow decelerations, turbulence enhancement and wake rotation. By comparing these turbulence characteristics to other turbulent structures in the atmospheric boundary layer, we found that convection driven eddies in the surface layer have similar turbulence characteristics as turbine wakes, which makes convective weather situations relevant for wind turbine fatigue considerations.     

Validation of the dynamic wake meander model for loads and power production in the Egmond aan Zee wind farm

This paper investigates wake effects on load and power production by using the dynamic wake meander (DWM) model implemented in the aeroelastic code HAWC2. The instationary wind farm flow characteristics are modeled by treating the wind turbine wakes as passive tracers transported downstream using a meandering process driven by the low frequent cross‐wind turbulence components. The model complex is validated by comparing simulated and measured loads for the Dutch Egmond aan Zee wind farm consisting of 36 Vestas V90 turbine located outside the coast of the Netherlands. Loads and production are compared for two distinct wind directions—a free wind situation from the dominating southwest and a full wake situation from northwest, where the observed turbine is operating in wake from five turbines in a row with 7D spacing. The measurements have a very high quality, allowing for detailed comparison of both fatigue and min–mean–max loads for blade root flap, tower yaw and tower bottom bending moments, respectively. Since the observed turbine is located deep inside a row of turbines, a new method on how to handle multiple wakes interaction is proposed. The agreement between measurements and simulations is excellent regarding power production in both free and wake sector, and a very good agreement is seen for the load comparisons too. This enables the conclusion that wake meandering, caused by large scale ambient turbulence, is indeed an important contribution to wake loading in wind farms. Copyright © 2012 John Wiley & Sons, Ltd.     

Combining economic and fluid dynamic models to determine the optimal spacing in very large wind farms

Wind turbine spacing is an important design parameter for wind farms. Placing turbines too close together reduces their power extraction because of wake effects and increases maintenance costs because of unsteady loading. Conversely, placing them further apart increases land and cabling costs, as well as electrical resistance losses. The asymptotic limit of very large wind farms in which the flow conditions can be considered ‘fully developed’ provides a useful framework for studying general trends in optimal layouts as a function of dimensionless cost parameters. Earlier analytical work by Meyers and Meneveau (Wind Energy 15, 305–317 (2012)) revealed that in the limit of very large wind farms, the optimal turbine spacing accounting for the turbine and land costs is significantly larger than the value found in typical existing wind farms. Here, we generalize the analysis to include effects of cable and maintenance costs upon optimal wind turbine spacing in very large wind farms under various economic criteria. For marginally profitable wind farms, minimum cost and maximum profit turbine spacings coincide. Assuming linear‐based and area‐based costs that are representative of either offshore or onshore sites we obtain for very large wind farms spacings that tend to be appreciably greater than occurring in actual farms confirming earlier results but now including cabling costs. However, we show later that if wind farms are highly profitable then optimization of the profit per unit area leads to tighter optimal spacings than would be implied by cost minimization. In addition, we investigate the influence of the type of wind farm layout. © 2016 The Authors Wind Energy Published by John Wiley & Sons Ltd     

The effects of array configuration on the hydro-environmental impacts of tidal turbines

The economic viability of tidal turbines will require the deployment of multiple devices in array formations in a manner analogous to wind farms. This research investigates the effects of the configuration of a tidal turbine array, specifically the turbine spacing and capacity, on the hydro-environmental impacts of the array. The hydrodynamic regime of the Shannon Estuary, a highly energetic estuary on the west coast of Ireland, was simulated using a depth integrated 2D hydro-environmental model. The numerical model was modified to incorporate the mechanics of energy extraction using linear momentum actuator disc theory and the impacts of a multiple device array were simulated. Three different array configurations were examined with turbine spacings of 0.5, 2 and 5 rotor diameters. The model results demonstrate that flows are attenuated inside the array and accelerated around the array. Water levels are also affected with a reduction in tidal range within, and upstream of, the array and a delay in high and low tides upstream of the array. The magnitude and extent of the observed impacts are found to reduce as the density and capacity are increased and that the impacts of large-scale arrays can be acceptable if deployed using a low density spacing of 5 rotor diameters.     

Wind-Turbine Model for System Simulations Near Cut-In Wind Speed

This paper presents a wind-turbine model for energy capture and switching simulation at lull wind conditions. The model includes aerodynamics as well as the control parts. It allows to study turbine behavior dependent on different controller settings and wind-speed characteristics. Based on such simulations, control parameters can be optimized regarding energy capture and turbine profits near cut-in wind speed. This was applied to a standard 1.5-MW wind turbine. Model validation was done using measurement data of different wind turbines. The model is kept as simple as possible considering the modeling of system components. However, all simplifications taken are allowable for energy capture and switching simulation. They guarantee shortest simulation times.     

An experimental investigation on the wake interferences among wind turbines sited in aligned and staggered wind farms

An experimental investigation was conducted for a better understanding of the wake interferences among wind turbines sited in wind farms with different turbine layout designs. Two different types of inflows were generated in an atmospheric boundary layer wind tunnel to simulate the different incoming surface winds over typical onshore and offshore wind farms. In addition to quantifying the power outputs and dynamic wind loads acting on the model turbines, the characteristics of the wake flows inside the wind farms were also examined quantitatively. After adding turbines staggered between the first 2 rows of an aligned wind farm to increase the turbine number density in the wind farm, the added staggered turbines did not show a significant effect on the aeromechanical performance of the downstream turbines for the offshore case. However, for the onshore case, while the upstream staggered turbines have a beneficial effect on the power outputs of the downstream turbines, the fatigue loads acting on the downstream turbines were also found to increase considerably due to the wake effects induced by the upstream turbines. With the same turbine number density and same inflow characteristics, the wind turbines were found to be able to generate much more power when they are arranged in a staggered layout than those in an aligned layout. In addition, the characteristics of the dynamic wind loads acting on the wind turbines sited in the aligned layout, including the fluctuation amplitudes and power spectrum, were found to be significantly different from those with staggered layout.     

Wind tunnel study on wind and turbulence intensity profiles in wind turbine wake

In recent years, there has been a rapid development of the wind farms in Japan. It becomes very important to investigate the wind turbine arrangement in wind farm, in order that the wake of one wind turbine does not to interfere with the flow in other wind turbines. In such a case, in order to achieve the highest possible efficiency from the wind, and to install as many as possible wind turbines within a limited area, it becomes a necessity to study the mutual interference of the wake developed by wind turbines. However, there is no report related to the effect of the turbulence intensity of the external flow on the wake behind a wind turbine generated in the wind tunnel. In this paper, the measurement results of the averaged wind profile and turbulence intensity profile in the wake in the wind tunnel are shown when the turbulence intensity of the external wind was changed. The wind tunnel experiment is performed with 500mm-diameter two-bladed horizontal axis wind turbine and the wind velocity in wake is measured by an I-type hot wire probe. As a result, it is clarified that high turbulence intensities enable to the entrainment of the main flow and the wake and to recover quickly the velocity in the wake.     

A new method for spatial allocation of turbines in a wind farm based on lightning protection efficiency

Existing studies of the spatial allocation of wind farms are typically based on turbine power generation efficiency and rarely consider the damage caused by lightning strikes. However, lightning damage seriously affects the economic performance of wind farms because of the high cost of repairing or replacing damaged blades. This paper proposes a method for the spatial optimization of multiple turbines based on lightning protection dependability. Firstly, the lightning protection efficiency of turbine blade protection systems is analyzed by combining the physical mechanisms of lightning leader progression with a conventional electro‐geometric model to develop an electro‐geometric model of turbine blades (EGMTB). Then, the optimized spatial allocation of multiple turbines in a wind farm is investigated using the EGMTB. The results are illustrated from an example wind farm with 1.5 MW turbines, which shows that the optimal spacing between two turbines perpendicular to the prevailing wind direction L_⊥ is 4R‐6R, where R is the length of a turbine blade. This spacing is shown to effectively shield turbine blades from lightning damage over a wide range of lightning currents (>26‐60 kA). Note that, the suggested L_⊥ will be smaller considering the influence of lightning polarity as it takes more difficulty developing upward leader (UL) in the condition of positive lightning striking. Experiments verify the effectiveness and correctness of this method.     

A wind‐tunnel study of the wake development behind wind turbines over sinusoidal hills

In the present work, the wake development behind small‐scale wind turbines is studied when introducing local topography variations consisting of a series of sinusoidal hills. Additionally, wind‐tunnel tests with homogeneous and sheared turbulent inflows were performed to understand how shear and ambient turbulence influence the results. The scale of the wind‐turbine models was about 1000 times smaller than full‐size turbines, suggesting that the present results should only be qualitatively extrapolated to real‐field scenarios. Wind‐tunnel measurements were made by means of stereoscopic particle image velocimetry to characterize the flow velocity in planes perpendicular to the flow direction. Over flat terrain, the wind‐turbine wake was seen to slowly approach the ground while it propagated downstream. When introducing hilly terrain, the downward wake deflection was enhanced in response to flow variations induced by the hills, and the turbulent kinetic energy content in the wake increased because of the speed‐up seen over the hills. The combined wake observed behind 2 streamwise aligned turbines was more diffused and when introducing hills, it was more prone to deflect towards the ground compared to the wake behind an isolated turbine. Since wake interactions are common at sites with multiple turbines, this suggested that it is important to consider the local hill‐induced velocity variations when onshore wind farms are analysed. Differences in the flow fields were seen when introducing either homogeneous or sheared turbulent inflow conditions, emphasizing the importance of accounting for the prevailing turbulence conditions at a given wind‐farm site to accurately capture the downstream wake development.     

Wind energy development and its environmental impact: A review

Wind energy, commonly recognized to be a clean and environmentally friendly renewable energy resource that can reduce our dependency on fossil fuels, has developed rapidly in recent years. Its mature technology and comparatively low cost make it promising as an important primary energy source in the future. However, there are potential environmental impacts due to the installation and operation of the wind turbines that cannot be ignored. This paper aims to provide an overview of world wind energy scenarios, the current status of wind turbine development, development trends of offshore wind farms, and the environmental and climatic impact of wind farms. The wake effect of wind turbines and modeling studies regarding this effect are also reviewed.     

Sensitivity of southern California wind energy to turbine characteristics

Using output from a high‐resolution meteorological simulation, we evaluate the sensitivity of southern California wind energy generation to variations in key characteristics of current wind turbines. These characteristics include hub height, rotor diameter and rated power, and depend on turbine make and model. They shape the turbine's power curve and thus have large implications for the energy generation capacity of wind farms. For each characteristic, we find complex and substantial geographical variations in the sensitivity of energy generation. However, the sensitivity associated with each characteristic can be predicted by a single corresponding climate statistic, greatly simplifying understanding of the relationship between climate and turbine optimization for energy production. In the case of the sensitivity to rotor diameter, the change in energy output per unit change in rotor diameter at any location is directly proportional to the weighted average wind speed between the cut‐in speed and the rated speed. The sensitivity to rated power variations is likewise captured by the percent of the wind speed distribution between the turbines rated and cut‐out speeds. Finally, the sensitivity to hub height is proportional to lower atmospheric wind shear. Using a wind turbine component cost model, we also evaluate energy output increase per dollar investment in each turbine characteristic. We find that rotor diameter increases typically provide a much larger wind energy boost per dollar invested, although there are some zones where investment in the other two characteristics is competitive. Our study underscores the need for joint analysis of regional climate, turbine engineering and economic modeling to optimize wind energy production. Copyright © 2012 John Wiley & Sons, Ltd.     

Coordinated control of a hybrid type 3 wind turbine and hydrogen energy storage model to provide efficient frequency control

The growing share of generation from wind farms is becoming one of the challenges in maintaining the sustainability of electric power systems. System operators approve requirements for the participation of such plants in frequency and power regulation, but they do not contain requirements for specific technologies in the control of wind turbines. There are several methods of frequency and power control, which are implemented by additional control systems, the implementation of underload mode, extraction of hidden inertia, the use of energy storage devices, etc. Each of these methods has both advantages and disadvantages. In this paper we consider the combined coordinated control of type 3 wind turbines using kinetic energy and energy from hydrogen storage to provide the best frequency response in order to minimize the negative factors. A digital-analog-physical model of type 3 wind turbine is used as a model, which allows to reproduce the whole range of transients most accurately and avoid the limitations of strictly numerical simulation.     

Effect of winds in a mountain pass on turbine performance

Mountain passes are potentially advantageous sites for the deployment of wind turbines because of road links and electrical transmission infrastructure. However, relatively little is known about wind characteristics and turbine response in these environments. Using hub height wind data from a mountain pass in Switzerland, this paper discusses the causes of the observed pass winds and how a generic wind turbine might perform in those conditions. During 3 months of winter measurements, the winds in the pass showed signatures of forcing by regional pressure gradients rather than local cooling or heating. Turbulence intensity was often less than 10%, and the magnitude of the wind shear power law exponent was less than 0.1. To understand the impact of pass winds on a wind turbine, we simulated a Wind Partnership for Advanced Component Technologies 1.5 MW wind turbine using the Fatigue, Aerodynamics, Structures, and Turbulence (FAST) aeroelastic simulator , forced by artificial wind fields of varying turbulence intensity and shear generated by the turbulence simulator TurbSim. We used the turbine simulation data to train a regression model that is used to predict the turbine response to the pass wind time series. Results showed that depending on long‐term wind characteristics, wind turbines in the pass may perform differently than predicted using a power curve derived from test measurements at another location. This method of generating site‐specific energy capture predictions could be combined with long‐term wind resource data and specific turbine models to better predict the energy production and turbine loads at this, or any other site. Copyright © 2013 John Wiley & Sons, Ltd.     

Aggregated dynamic model for wind farms with doubly fed induction generator wind turbines

As a result of increasing wind farms penetration in power systems, the wind farms begin to influence power system, and thus the modelling of wind farms has become an interesting research topic. Nowadays, doubly fed induction generator based on wind turbine is the most widely used technology for wind farms due to its main advantages such as high-energy efficiency and controllability, and improved power quality. When the impact of a wind farm on power systems is studied, the behavior of the wind farm at the point common coupling to grid can be represented by an equivalent model derived from the aggregation of wind turbines into an equivalent wind turbine, instead of the complete model including the modelling of all the wind turbines. In this paper, a new equivalent model of wind farms with doubly fed induction generator wind turbines is proposed to represent the collective response of the wind farm by one single equivalent wind turbine, even although the aggregated wind turbines operate receiving different incoming winds. The effectiveness of the equivalent model to represent the collective response of the wind farm is demonstrated by comparing the simulation results of equivalent and complete models both during normal operation and grid disturbances.